Dynamical Information Geometry (DIG), Part IV: Regime Tests and Invariance — Data Set

This dataset accompanies Dynamical Information Geometry (DIG), Part IV and provides the complete numerical and hardware data used to investigate the regime structure, validity boundaries, and structural invariance properties of the DIG framework. DIG assigns an effective, state-dependent geometry to quantum many-body systems via the curvature of a coarse-grained mutual-information profile. While DIG Part I establishes the theoretical framework, DIG Part II provides numerical evidence for slowing and acceleration effects, and DIG Part III validates a minimal operational consequence on quantum hardware, the present dataset supports DIG Part IV by documenting the stability and invariance properties of these sign-dependent modifications of operator propagation under controlled variations. The dataset includes raw and processed data from a collection of operationally defined tests performed under strictly energy-matched conditions. These tests probe sign structure, antisymmetry, regime boundaries, invariance under changes in system size or implementation, and robustness under local perturbations. Both numerical simulations and quantum-hardware executions are included where applicable. All data are provided without fitting, extrapolation, noise mitigation, or cross-platform normalization beyond the explicitly documented operational definitions. The archive is designed to enable independent verification, alternative analyses under clearly stated assumptions, and reproducibility audits. The dataset contains complete raw outputs, analysis and audit scripts, metric inventories, regime tables, and a detailed README describing folder structure, operational definitions, and verification procedures. Cryptographic checksums (SHA-256) are provided separately to ensure data integrity. Relation to the DIG program DIG Part I (theoretical framework):https://doi.org/10.5281/zenodo.17983399 DIG Part II (numerical validation):https://doi.org/10.5281/zenodo.17982058 DIG Part III (hardware validation):https://doi.org/10.5281/zenodo.18100057 DIG — N1 (definitions and scope):https://doi.org/10.5281/zenodo.18001179 DIG Part IV introduces no new theoretical constructs beyond these works. The dataset is intended to document the regime behavior and structural robustness of the DIG framework in an auditable and reproducible manner. Intended use This dataset is intended for independent verification of regime behavior, reproducibility checks, and comparative analysis under explicit operational choices. It is not intended as a benchmark for quantitative universality or parameter fitting. Correspondence regarding this dataset may be directed to: [e-mail]本数据集随《动态信息几何（Dynamical Information Geometry, DIG）》第四部分一同发布，提供了完整的数值与硬件数据，用于探究DIG框架的相区结构、有效性边界以及结构不变性特性。 DIG通过粗粒化互信息分布的曲率，为量子多体系统赋予了有效且依赖于状态的几何结构。其中，DIG第一部分构建了该理论框架，第二部分提供了关于减速与加速效应的数值证据，第三部分验证了量子硬件上的最小操作效应；本数据集则支撑DIG第四部分的研究，记录了在受控变量变化下，算子传播的这些与符号相关的修正项的稳定性与不变性特性。 本数据集包含在严格能量匹配条件下开展的多组操作化定义测试的原始与处理后数据。这些测试用于探究符号结构、反对称性、相区边界、系统规模或实现方式变化下的不变性，以及局部扰动下的鲁棒性。在适用场景下，数据集同时涵盖数值模拟与量子硬件运行结果。 所有数据均未经过拟合、外推、噪声抑制或跨平台归一化处理，仅遵循明确文档化的操作定义。该归档包旨在支持独立验证、基于明确假设的替代分析，以及可重复性审核。 本数据集包含完整的原始输出文件、分析与审核脚本、指标清单、相区表格，以及一份详细的README文档，用于说明文件夹结构、操作定义与验证流程。此外还单独提供了加密校验和（SHA-256）以保障数据完整性。 与DIG研究计划的关联 DIG第一部分（理论框架）：https://doi.org/10.5281/zenodo.17983399 DIG第二部分（数值验证）：https://doi.org/10.5281/zenodo.17982058 DIG第三部分（硬件验证）：https://doi.org/10.5281/zenodo.18100057 DIG — N1（定义与范围）：https://doi.org/10.5281/zenodo.18001179 DIG第四部分未在上述研究基础上引入新的理论构建。本数据集旨在以可审核、可复现的方式，记录DIG框架的相区行为与结构鲁棒性。 预期用途 本数据集旨在用于相区行为的独立验证、可重复性检查，以及基于明确操作选择的对比分析。本数据集并非用于定量普适性或参数拟合的基准测试集。 关于本数据集的相关联络可发送至：[e-mail]